SOLUTION: Rebecca owns three houses and makes money by renting them out. She charges three times as much per month for the second house than the first. The monthly rent for the third house i

Question 486846: Rebecca owns three houses and makes money by renting them out. She charges three times as much per month for the second house than the first. The monthly rent for the third house is one thousand, eight hundred dollars less than the sum of the monthly rents for the first two houses. The first house was vacant for five months, but otherwise rents were received every month from the tenants of the three houses. Rebecca had total rent receipts of $60,300 for the year. How much, per month, was the rent for the third house?
Answer by MathTherapy(10557) (Show Source): You can put this solution on YOUR website!
Rebecca owns three houses and makes money by renting them out. She charges three times as much per month for the second house than the first. The monthly rent for the third house is one thousand, eight hundred dollars less than the sum of the monthly rents for the first two houses. The first house was vacant for five months, but otherwise rents were received every month from the tenants of the three houses. Rebecca had total rent receipts of $60,300 for the year. How much, per month, was the rent for the third house?

Let the rent, per month for the first house be F
Then the rent, per month for the second house is 3F, and the rent for the third house is (F + 3F) - 1,800, or 4F - 1,800

Now, since during the year she only collected 7 months' rent for the first house, then for the year she received 7 * F, or 7F

Since she collected 12 months' rent for the second house, then for the year she received 12 * 3F, or 36F

Since she collected 12 months' rent for the third house, then for the year she received 12 * (4F - 1,800), or 48F - 21,600

Now, since she received a total of $60,300 during the year for rent, then we can say that:

7F + 36F + 48F - 21,600 = 60,300

91F = 60,300 + 21,600

91F = 81,900

F, or rent, per month for the first house is: = $900

Since she received (4F - 1,800), per month for the third house, then for the third house, she receives: 4*900 - 1,800, or $3,600 - 1,800 = $

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